TSTP Solution File: SEV001^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV001^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 18:04:23 EDT 2022
% Result : Theorem 83.35s 83.19s
% Output : Proof 83.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 177
% Syntax : Number of formulae : 577 ( 202 unt; 9 typ; 0 def)
% Number of atoms : 2693 ( 323 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 3186 ( 453 ~; 305 |; 0 &;2308 @)
% ( 0 <=>; 118 =>; 2 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 97 ( 95 usr; 94 con; 0-2 aty)
% Number of variables : 437 ( 0 ^ 437 !; 0 ?; 437 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > a ).
thf(ty_eigen__0,type,
eigen__0: a > a > a ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(cDISTRIB_THM_pme,conjecture,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ( ( ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
= ( ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ( ( ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
= ( ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cDISTRIB_THM_pme]) ).
thf(h1,assumption,
~ ! [X1: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ X2 @ X2 )
= X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ( eigen__0 @ ( eigen__0 @ X2 @ X3 ) @ X4 )
= ( eigen__0 @ X2 @ ( eigen__0 @ X3 @ X4 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) ) )
=> ~ ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
= ( eigen__0 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( eigen__0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 ) )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ ( eigen__0 @ X2 @ X3 ) @ X3 )
= X3 ) )
=> ( ( ! [X2: a,X3: a,X4: a] :
( ( eigen__0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X2 @ X3 ) @ ( eigen__0 @ X2 @ X4 ) ) ) )
= ( ! [X2: a,X3: a,X4: a] :
( ( X1 @ X2 @ ( eigen__0 @ X3 @ X4 ) )
= ( eigen__0 @ ( X1 @ X2 @ X3 ) @ ( X1 @ X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ( ( ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ X3 ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ ( eigen__0 @ X1 @ X3 ) ) ) )
= ( ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ X1 @ ( eigen__0 @ X2 @ X3 ) )
= ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ ( eigen__1 @ X1 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ X3 ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ ( eigen__0 @ X1 @ X3 ) ) ) )
!= ( ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ X1 @ ( eigen__0 @ X2 @ X3 ) )
= ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ ( eigen__1 @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 ),
introduced(assumption,[]) ).
thf(h18,assumption,
! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ),
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ X3 ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ ( eigen__0 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ X1 @ ( eigen__0 @ X2 @ X3 ) )
= ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ ( eigen__1 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ X3 ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ ( eigen__0 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ X1 @ ( eigen__0 @ X2 @ X3 ) )
= ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ ( eigen__1 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__1 @ eigen__2 @ ( eigen__0 @ X1 @ X2 ) )
= ( eigen__0 @ ( eigen__1 @ eigen__2 @ X1 ) @ ( eigen__1 @ eigen__2 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: a] :
( ( eigen__1 @ eigen__2 @ ( eigen__0 @ eigen__3 @ X1 ) )
= ( eigen__0 @ ( eigen__1 @ eigen__2 @ eigen__3 ) @ ( eigen__1 @ eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
( eigen__1 @ eigen__2 @ ( eigen__0 @ eigen__3 @ eigen__4 ) )
!= ( eigen__0 @ ( eigen__1 @ eigen__2 @ eigen__3 ) @ ( eigen__1 @ eigen__2 @ eigen__4 ) ),
introduced(assumption,[]) ).
thf(ax1140,axiom,
( ~ p6
| p53 ),
file('<stdin>',ax1140) ).
thf(ax1171,axiom,
( ~ p2
| p22 ),
file('<stdin>',ax1171) ).
thf(ax811,axiom,
( ~ p53
| p382 ),
file('<stdin>',ax811) ).
thf(ax1188,axiom,
p6,
file('<stdin>',ax1188) ).
thf(ax1147,axiom,
( ~ p5
| p46 ),
file('<stdin>',ax1147) ).
thf(ax1164,axiom,
( ~ p3
| p29 ),
file('<stdin>',ax1164) ).
thf(ax1139,axiom,
( ~ p6
| p54 ),
file('<stdin>',ax1139) ).
thf(ax1162,axiom,
( ~ p3
| p31 ),
file('<stdin>',ax1162) ).
thf(pax10,axiom,
( p10
=> ! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 ) ),
file('<stdin>',pax10) ).
thf(ax1059,axiom,
( ~ p22
| p134 ),
file('<stdin>',ax1059) ).
thf(ax1192,axiom,
p2,
file('<stdin>',ax1192) ).
thf(pax382,axiom,
( p382
=> ( ( f__0 @ f__3 @ f__2 )
= ( f__0 @ f__2 @ f__3 ) ) ),
file('<stdin>',pax382) ).
thf(pax46,axiom,
( p46
=> ! [X1: a] :
( ( f__1 @ f__2 @ X1 )
= ( f__1 @ X1 @ f__2 ) ) ),
file('<stdin>',pax46) ).
thf(ax1189,axiom,
p5,
file('<stdin>',ax1189) ).
thf(ax1003,axiom,
( ~ p29
| p190 ),
file('<stdin>',ax1003) ).
thf(ax1191,axiom,
p3,
file('<stdin>',ax1191) ).
thf(ax1175,axiom,
( ~ p2
| p18 ),
file('<stdin>',ax1175) ).
thf(pax54,axiom,
( p54
=> ! [X1: a] :
( ( f__0 @ f__2 @ X1 )
= ( f__0 @ X1 @ f__2 ) ) ),
file('<stdin>',pax54) ).
thf(ax987,axiom,
( ~ p31
| p206 ),
file('<stdin>',ax987) ).
thf(ax1169,axiom,
( ~ p2
| p24 ),
file('<stdin>',ax1169) ).
thf(ax1138,axiom,
( ~ p6
| p55 ),
file('<stdin>',ax1138) ).
thf(pax6,axiom,
( p6
=> ! [X1: a,X2: a] :
( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) ) ),
file('<stdin>',pax6) ).
thf(ax1155,axiom,
( ~ p4
| p38 ),
file('<stdin>',ax1155) ).
thf(ax1121,axiom,
( ~ p8
| p72 ),
file('<stdin>',ax1121) ).
thf(ax128,axiom,
( ~ p12
| p880 ),
file('<stdin>',ax128) ).
thf(ax1124,axiom,
( ~ p8
| p69 ),
file('<stdin>',ax1124) ).
thf(ax1123,axiom,
( ~ p8
| p70 ),
file('<stdin>',ax1123) ).
thf(pax134,axiom,
( p134
=> ! [X1: a] :
( ( f__0 @ f__2 @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ ( f__0 @ f__2 @ f__2 ) @ ( f__0 @ f__2 @ X1 ) ) ) ),
file('<stdin>',pax134) ).
thf(ax1184,axiom,
p10,
file('<stdin>',ax1184) ).
thf(pax190,axiom,
( p190
=> ( ( f__1 @ ( f__0 @ f__3 @ f__2 ) @ f__2 )
= f__2 ) ),
file('<stdin>',pax190) ).
thf(ax1091,axiom,
( ~ p18
| p102 ),
file('<stdin>',ax1091) ).
thf(pax206,axiom,
( p206
=> ( ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 )
= f__2 ) ),
file('<stdin>',pax206) ).
thf(ax1043,axiom,
( ~ p24
| p150 ),
file('<stdin>',ax1043) ).
thf(pax55,axiom,
( p55
=> ! [X1: a] :
( ( f__0 @ f__4 @ X1 )
= ( f__0 @ X1 @ f__4 ) ) ),
file('<stdin>',pax55) ).
thf(pax38,axiom,
( p38
=> ! [X1: a] :
( ( f__0 @ ( f__1 @ f__2 @ X1 ) @ X1 )
= X1 ) ),
file('<stdin>',pax38) ).
thf(ax1190,axiom,
p4,
file('<stdin>',ax1190) ).
thf(ax658,axiom,
( ~ p72
| p535 ),
file('<stdin>',ax658) ).
thf(ax1186,axiom,
p8,
file('<stdin>',ax1186) ).
thf(ax1112,axiom,
( ~ p10
| p81 ),
file('<stdin>',ax1112) ).
thf(ax127,axiom,
( ~ p880
| p881 ),
file('<stdin>',ax127) ).
thf(ax1183,axiom,
p12,
file('<stdin>',ax1183) ).
thf(ax1176,axiom,
( ~ p2
| p17 ),
file('<stdin>',ax1176) ).
thf(ax1131,axiom,
( ~ p7
| p62 ),
file('<stdin>',ax1131) ).
thf(ax684,axiom,
( ~ p69
| p509 ),
file('<stdin>',ax684) ).
thf(ax1172,axiom,
( ~ p2
| p21 ),
file('<stdin>',ax1172) ).
thf(ax687,axiom,
( ~ p69
| p506 ),
file('<stdin>',ax687) ).
thf(ax679,axiom,
( ~ p70
| p514 ),
file('<stdin>',ax679) ).
thf(ax1148,axiom,
( ~ p5
| p45 ),
file('<stdin>',ax1148) ).
thf(pax8,axiom,
( p8
=> ! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) ),
file('<stdin>',pax8) ).
thf(pax102,axiom,
( p102
=> ! [X1: a] :
( ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ f__2 ) @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) ) ) ),
file('<stdin>',pax102) ).
thf(pax150,axiom,
( p150
=> ! [X1: a] :
( ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ f__2 ) @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ X1 ) ) ) ),
file('<stdin>',pax150) ).
thf(pax535,axiom,
( p535
=> ! [X1: a] :
( ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ f__4 ) @ X1 )
= ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ ( f__0 @ f__4 @ X1 ) ) ) ),
file('<stdin>',pax535) ).
thf(ax126,axiom,
( ~ p881
| ~ p81
| p879 ),
file('<stdin>',ax126) ).
thf(ax1100,axiom,
( ~ p17
| p93 ),
file('<stdin>',ax1100) ).
thf(pax9,axiom,
( p9
=> ! [X1: a] :
( ( f__1 @ X1 @ X1 )
= X1 ) ),
file('<stdin>',pax9) ).
thf(ax739,axiom,
( ~ p62
| p454 ),
file('<stdin>',ax739) ).
thf(ax1187,axiom,
p7,
file('<stdin>',ax1187) ).
thf(ax1134,axiom,
( ~ p7
| p59 ),
file('<stdin>',ax1134) ).
thf(pax5,axiom,
( p5
=> ! [X1: a,X2: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ) ),
file('<stdin>',pax5) ).
thf(pax509,axiom,
( p509
=> ! [X1: a] :
( ( f__0 @ ( f__0 @ f__3 @ f__3 ) @ X1 )
= ( f__0 @ f__3 @ ( f__0 @ f__3 @ X1 ) ) ) ),
file('<stdin>',pax509) ).
thf(pax21,axiom,
( p21
=> ! [X1: a,X2: a] :
( ( f__0 @ f__3 @ ( f__1 @ X1 @ X2 ) )
= ( f__1 @ ( f__0 @ f__3 @ X1 ) @ ( f__0 @ f__3 @ X2 ) ) ) ),
file('<stdin>',pax21) ).
thf(ax1069,axiom,
( ~ p21
| p124 ),
file('<stdin>',ax1069) ).
thf(pax4,axiom,
( p4
=> ! [X1: a,X2: a] :
( ( f__0 @ ( f__1 @ X1 @ X2 ) @ X2 )
= X2 ) ),
file('<stdin>',pax4) ).
thf(nax1,axiom,
( p1
<= ( ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) )
= ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) ) ),
file('<stdin>',nax1) ).
thf(ax1193,axiom,
~ p1,
file('<stdin>',ax1193) ).
thf(pax506,axiom,
( p506
=> ! [X1: a] :
( ( f__0 @ ( f__0 @ f__3 @ ( f__1 @ f__2 @ f__3 ) ) @ X1 )
= ( f__0 @ f__3 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) ) ) ),
file('<stdin>',pax506) ).
thf(pax514,axiom,
( p514
=> ! [X1: a] :
( ( f__0 @ ( f__0 @ f__2 @ ( f__1 @ f__2 @ f__3 ) ) @ X1 )
= ( f__0 @ f__2 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) ) ) ),
file('<stdin>',pax514) ).
thf(pax45,axiom,
( p45
=> ! [X1: a] :
( ( f__1 @ f__3 @ X1 )
= ( f__1 @ X1 @ f__3 ) ) ),
file('<stdin>',pax45) ).
thf(pax879,axiom,
( p879
=> ( ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) )
= ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) ) ) ),
file('<stdin>',pax879) ).
thf(ax37,axiom,
( ~ p93
| p962 ),
file('<stdin>',ax37) ).
thf(pax454,axiom,
( p454
=> ! [X1: a] :
( ( f__1 @ ( f__1 @ f__2 @ f__2 ) @ X1 )
= ( f__1 @ f__2 @ ( f__1 @ f__2 @ X1 ) ) ) ),
file('<stdin>',pax454) ).
thf(ax1185,axiom,
p9,
file('<stdin>',ax1185) ).
thf(pax7,axiom,
( p7
=> ! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__1 @ X1 @ X2 ) @ X3 )
= ( f__1 @ X1 @ ( f__1 @ X2 @ X3 ) ) ) ),
file('<stdin>',pax7) ).
thf(ax763,axiom,
( ~ p59
| p430 ),
file('<stdin>',ax763) ).
thf(pax3,axiom,
( p3
=> ! [X1: a,X2: a] :
( ( f__1 @ ( f__0 @ X1 @ X2 ) @ X2 )
= X2 ) ),
file('<stdin>',pax3) ).
thf(pax124,axiom,
( p124
=> ! [X1: a] :
( ( f__0 @ f__3 @ ( f__1 @ ( f__0 @ f__3 @ f__4 ) @ X1 ) )
= ( f__1 @ ( f__0 @ f__3 @ ( f__0 @ f__3 @ f__4 ) ) @ ( f__0 @ f__3 @ X1 ) ) ) ),
file('<stdin>',pax124) ).
thf(pax962,axiom,
( p962
=> ( ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ ( f__1 @ f__3 @ f__2 ) )
= ( f__1 @ ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ f__3 ) @ ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ f__2 ) ) ) ),
file('<stdin>',pax962) ).
thf(pax430,axiom,
( p430
=> ! [X1: a] :
( ( f__1 @ ( f__1 @ ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ) @ f__2 ) @ X1 )
= ( f__1 @ ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ) @ ( f__1 @ f__2 @ X1 ) ) ) ),
file('<stdin>',pax430) ).
thf(pax2,axiom,
( p2
=> ! [X1: a,X2: a,X3: a] :
( ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) ) ),
file('<stdin>',pax2) ).
thf(c_0_79,plain,
( ~ p6
| p53 ),
inference(fof_simplification,[status(thm)],[ax1140]) ).
thf(c_0_80,plain,
( ~ p2
| p22 ),
inference(fof_simplification,[status(thm)],[ax1171]) ).
thf(c_0_81,plain,
( ~ p53
| p382 ),
inference(fof_simplification,[status(thm)],[ax811]) ).
thf(c_0_82,plain,
( p53
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_83,plain,
p6,
inference(split_conjunct,[status(thm)],[ax1188]) ).
thf(c_0_84,plain,
( ~ p5
| p46 ),
inference(fof_simplification,[status(thm)],[ax1147]) ).
thf(c_0_85,plain,
( ~ p3
| p29 ),
inference(fof_simplification,[status(thm)],[ax1164]) ).
thf(c_0_86,plain,
( ~ p6
| p54 ),
inference(fof_simplification,[status(thm)],[ax1139]) ).
thf(c_0_87,plain,
( ~ p3
| p31 ),
inference(fof_simplification,[status(thm)],[ax1162]) ).
thf(c_0_88,plain,
! [X804: a] :
( ~ p10
| ( ( f__0 @ X804 @ X804 )
= X804 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])]) ).
thf(c_0_89,plain,
( ~ p22
| p134 ),
inference(fof_simplification,[status(thm)],[ax1059]) ).
thf(c_0_90,plain,
( p22
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_91,plain,
p2,
inference(split_conjunct,[status(thm)],[ax1192]) ).
thf(c_0_92,plain,
( ~ p382
| ( ( f__0 @ f__3 @ f__2 )
= ( f__0 @ f__2 @ f__3 ) ) ),
inference(fof_nnf,[status(thm)],[pax382]) ).
thf(c_0_93,plain,
( p382
| ~ p53 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
thf(c_0_94,plain,
p53,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83])]) ).
thf(c_0_95,plain,
! [X720: a] :
( ~ p46
| ( ( f__1 @ f__2 @ X720 )
= ( f__1 @ X720 @ f__2 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax46])])]) ).
thf(c_0_96,plain,
( p46
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_97,plain,
p5,
inference(split_conjunct,[status(thm)],[ax1189]) ).
thf(c_0_98,plain,
( ~ p29
| p190 ),
inference(fof_simplification,[status(thm)],[ax1003]) ).
thf(c_0_99,plain,
( p29
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
thf(c_0_100,plain,
p3,
inference(split_conjunct,[status(thm)],[ax1191]) ).
thf(c_0_101,plain,
( ~ p2
| p18 ),
inference(fof_simplification,[status(thm)],[ax1175]) ).
thf(c_0_102,plain,
! [X704: a] :
( ~ p54
| ( ( f__0 @ f__2 @ X704 )
= ( f__0 @ X704 @ f__2 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax54])])]) ).
thf(c_0_103,plain,
( p54
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
thf(c_0_104,plain,
( ~ p31
| p206 ),
inference(fof_simplification,[status(thm)],[ax987]) ).
thf(c_0_105,plain,
( p31
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
thf(c_0_106,plain,
( ~ p2
| p24 ),
inference(fof_simplification,[status(thm)],[ax1169]) ).
thf(c_0_107,plain,
( ~ p6
| p55 ),
inference(fof_simplification,[status(thm)],[ax1138]) ).
thf(c_0_108,plain,
! [X820: a,X821: a] :
( ~ p6
| ( ( f__0 @ X820 @ X821 )
= ( f__0 @ X821 @ X820 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])]) ).
thf(c_0_109,plain,
( ~ p4
| p38 ),
inference(fof_simplification,[status(thm)],[ax1155]) ).
thf(c_0_110,plain,
( ~ p8
| p72 ),
inference(fof_simplification,[status(thm)],[ax1121]) ).
thf(c_0_111,plain,
( ~ p12
| p880 ),
inference(fof_simplification,[status(thm)],[ax128]) ).
thf(c_0_112,plain,
( ~ p8
| p69 ),
inference(fof_simplification,[status(thm)],[ax1124]) ).
thf(c_0_113,plain,
( ~ p8
| p70 ),
inference(fof_simplification,[status(thm)],[ax1123]) ).
thf(c_0_114,plain,
! [X544: a] :
( ~ p134
| ( ( f__0 @ f__2 @ ( f__1 @ f__2 @ X544 ) )
= ( f__1 @ ( f__0 @ f__2 @ f__2 ) @ ( f__0 @ f__2 @ X544 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax134])])]) ).
thf(c_0_115,plain,
! [X1: a] :
( ( ( f__0 @ X1 @ X1 )
= X1 )
| ~ p10 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
thf(c_0_116,plain,
p10,
inference(split_conjunct,[status(thm)],[ax1184]) ).
thf(c_0_117,plain,
( p134
| ~ p22 ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
thf(c_0_118,plain,
p22,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
thf(c_0_119,plain,
( ~ p190
| ( ( f__1 @ ( f__0 @ f__3 @ f__2 ) @ f__2 )
= f__2 ) ),
inference(fof_nnf,[status(thm)],[pax190]) ).
thf(c_0_120,plain,
( ( ( f__0 @ f__3 @ f__2 )
= ( f__0 @ f__2 @ f__3 ) )
| ~ p382 ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
thf(c_0_121,plain,
p382,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
thf(c_0_122,plain,
! [X1: a] :
( ( ( f__1 @ f__2 @ X1 )
= ( f__1 @ X1 @ f__2 ) )
| ~ p46 ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
thf(c_0_123,plain,
p46,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]) ).
thf(c_0_124,plain,
( p190
| ~ p29 ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
thf(c_0_125,plain,
p29,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100])]) ).
thf(c_0_126,plain,
( ~ p18
| p102 ),
inference(fof_simplification,[status(thm)],[ax1091]) ).
thf(c_0_127,plain,
( p18
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
thf(c_0_128,plain,
( ~ p206
| ( ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 )
= f__2 ) ),
inference(fof_nnf,[status(thm)],[pax206]) ).
thf(c_0_129,plain,
! [X1: a] :
( ( ( f__0 @ f__2 @ X1 )
= ( f__0 @ X1 @ f__2 ) )
| ~ p54 ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
thf(c_0_130,plain,
p54,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_83])]) ).
thf(c_0_131,plain,
( p206
| ~ p31 ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
thf(c_0_132,plain,
p31,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_100])]) ).
thf(c_0_133,plain,
( ~ p24
| p150 ),
inference(fof_simplification,[status(thm)],[ax1043]) ).
thf(c_0_134,plain,
( p24
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
thf(c_0_135,plain,
! [X702: a] :
( ~ p55
| ( ( f__0 @ f__4 @ X702 )
= ( f__0 @ X702 @ f__4 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax55])])]) ).
thf(c_0_136,plain,
( p55
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
thf(c_0_137,plain,
! [X736: a] :
( ~ p38
| ( ( f__0 @ ( f__1 @ f__2 @ X736 ) @ X736 )
= X736 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax38])])]) ).
thf(c_0_138,plain,
! [X2: a,X1: a] :
( ( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) )
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
thf(c_0_139,plain,
( p38
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
thf(c_0_140,plain,
p4,
inference(split_conjunct,[status(thm)],[ax1190]) ).
thf(c_0_141,plain,
( ~ p72
| p535 ),
inference(fof_simplification,[status(thm)],[ax658]) ).
thf(c_0_142,plain,
( p72
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
thf(c_0_143,plain,
p8,
inference(split_conjunct,[status(thm)],[ax1186]) ).
thf(c_0_144,plain,
( ~ p10
| p81 ),
inference(fof_simplification,[status(thm)],[ax1112]) ).
thf(c_0_145,plain,
( ~ p880
| p881 ),
inference(fof_simplification,[status(thm)],[ax127]) ).
thf(c_0_146,plain,
( p880
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
thf(c_0_147,plain,
p12,
inference(split_conjunct,[status(thm)],[ax1183]) ).
thf(c_0_148,plain,
( ~ p2
| p17 ),
inference(fof_simplification,[status(thm)],[ax1176]) ).
thf(c_0_149,plain,
( ~ p7
| p62 ),
inference(fof_simplification,[status(thm)],[ax1131]) ).
thf(c_0_150,plain,
( ~ p69
| p509 ),
inference(fof_simplification,[status(thm)],[ax684]) ).
thf(c_0_151,plain,
( p69
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_152,plain,
( ~ p2
| p21 ),
inference(fof_simplification,[status(thm)],[ax1172]) ).
thf(c_0_153,plain,
( ~ p69
| p506 ),
inference(fof_simplification,[status(thm)],[ax687]) ).
thf(c_0_154,plain,
( ~ p70
| p514 ),
inference(fof_simplification,[status(thm)],[ax679]) ).
thf(c_0_155,plain,
( p70
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_156,plain,
( ~ p5
| p45 ),
inference(fof_simplification,[status(thm)],[ax1148]) ).
thf(c_0_157,plain,
! [X808: a,X809: a,X810: a] :
( ~ p8
| ( ( f__0 @ ( f__0 @ X808 @ X809 ) @ X810 )
= ( f__0 @ X808 @ ( f__0 @ X809 @ X810 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])]) ).
thf(c_0_158,plain,
! [X608: a] :
( ~ p102
| ( ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ X608 ) )
= ( f__1 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ f__2 ) @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X608 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax102])])]) ).
thf(c_0_159,plain,
! [X1: a] :
( ( ( f__0 @ f__2 @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ ( f__0 @ f__2 @ f__2 ) @ ( f__0 @ f__2 @ X1 ) ) )
| ~ p134 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_160,plain,
! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116])]) ).
thf(c_0_161,plain,
p134,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]) ).
thf(c_0_162,plain,
( ( ( f__1 @ ( f__0 @ f__3 @ f__2 ) @ f__2 )
= f__2 )
| ~ p190 ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
thf(c_0_163,plain,
( ( f__0 @ f__3 @ f__2 )
= ( f__0 @ f__2 @ f__3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
thf(c_0_164,plain,
! [X1: a] :
( ( f__1 @ f__2 @ X1 )
= ( f__1 @ X1 @ f__2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])]) ).
thf(c_0_165,plain,
p190,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125])]) ).
thf(c_0_166,plain,
( p102
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
thf(c_0_167,plain,
p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_91])]) ).
thf(c_0_168,plain,
! [X512: a] :
( ~ p150
| ( ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ ( f__1 @ f__2 @ X512 ) )
= ( f__1 @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ f__2 ) @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ X512 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax150])])]) ).
thf(c_0_169,plain,
( ( ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 )
= f__2 )
| ~ p206 ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_170,plain,
! [X1: a] :
( ( f__0 @ f__2 @ X1 )
= ( f__0 @ X1 @ f__2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130])]) ).
thf(c_0_171,plain,
p206,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132])]) ).
thf(c_0_172,plain,
( p150
| ~ p24 ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
thf(c_0_173,plain,
p24,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_91])]) ).
thf(c_0_174,plain,
! [X254: a] :
( ~ p535
| ( ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ f__4 ) @ X254 )
= ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ ( f__0 @ f__4 @ X254 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax535])])]) ).
thf(c_0_175,plain,
! [X1: a] :
( ( ( f__0 @ f__4 @ X1 )
= ( f__0 @ X1 @ f__4 ) )
| ~ p55 ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
thf(c_0_176,plain,
p55,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_83])]) ).
thf(c_0_177,plain,
! [X1: a] :
( ( ( f__0 @ ( f__1 @ f__2 @ X1 ) @ X1 )
= X1 )
| ~ p38 ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
thf(c_0_178,plain,
! [X2: a,X1: a] :
( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_83])]) ).
thf(c_0_179,plain,
p38,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140])]) ).
thf(c_0_180,plain,
( p535
| ~ p72 ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
thf(c_0_181,plain,
p72,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_143])]) ).
thf(c_0_182,plain,
( ~ p881
| ~ p81
| p879 ),
inference(fof_simplification,[status(thm)],[ax126]) ).
thf(c_0_183,plain,
( p81
| ~ p10 ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_184,plain,
( p881
| ~ p880 ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
thf(c_0_185,plain,
p880,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147])]) ).
thf(c_0_186,plain,
( ~ p17
| p93 ),
inference(fof_simplification,[status(thm)],[ax1100]) ).
thf(c_0_187,plain,
( p17
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
thf(c_0_188,plain,
! [X806: a] :
( ~ p9
| ( ( f__1 @ X806 @ X806 )
= X806 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax9])])]) ).
thf(c_0_189,plain,
( ~ p62
| p454 ),
inference(fof_simplification,[status(thm)],[ax739]) ).
thf(c_0_190,plain,
( p62
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
thf(c_0_191,plain,
p7,
inference(split_conjunct,[status(thm)],[ax1187]) ).
thf(c_0_192,plain,
( ~ p7
| p59 ),
inference(fof_simplification,[status(thm)],[ax1134]) ).
thf(c_0_193,plain,
! [X824: a,X825: a] :
( ~ p5
| ( ( f__1 @ X824 @ X825 )
= ( f__1 @ X825 @ X824 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_194,plain,
! [X306: a] :
( ~ p509
| ( ( f__0 @ ( f__0 @ f__3 @ f__3 ) @ X306 )
= ( f__0 @ f__3 @ ( f__0 @ f__3 @ X306 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax509])])]) ).
thf(c_0_195,plain,
( p509
| ~ p69 ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
thf(c_0_196,plain,
p69,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_143])]) ).
thf(c_0_197,plain,
! [X776: a,X777: a] :
( ~ p21
| ( ( f__0 @ f__3 @ ( f__1 @ X776 @ X777 ) )
= ( f__1 @ ( f__0 @ f__3 @ X776 ) @ ( f__0 @ f__3 @ X777 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax21])])]) ).
thf(c_0_198,plain,
( p21
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
thf(c_0_199,plain,
( ~ p21
| p124 ),
inference(fof_simplification,[status(thm)],[ax1069]) ).
thf(c_0_200,plain,
! [X828: a,X829: a] :
( ~ p4
| ( ( f__0 @ ( f__1 @ X828 @ X829 ) @ X829 )
= X829 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])]) ).
thf(c_0_201,plain,
( ( ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) )
!= ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) )
| p1 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])]) ).
thf(c_0_202,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1193]) ).
thf(c_0_203,plain,
! [X312: a] :
( ~ p506
| ( ( f__0 @ ( f__0 @ f__3 @ ( f__1 @ f__2 @ f__3 ) ) @ X312 )
= ( f__0 @ f__3 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X312 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax506])])]) ).
thf(c_0_204,plain,
( p506
| ~ p69 ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
thf(c_0_205,plain,
! [X296: a] :
( ~ p514
| ( ( f__0 @ ( f__0 @ f__2 @ ( f__1 @ f__2 @ f__3 ) ) @ X296 )
= ( f__0 @ f__2 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X296 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax514])])]) ).
thf(c_0_206,plain,
( p514
| ~ p70 ),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
thf(c_0_207,plain,
p70,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_143])]) ).
thf(c_0_208,plain,
! [X722: a] :
( ~ p45
| ( ( f__1 @ f__3 @ X722 )
= ( f__1 @ X722 @ f__3 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax45])])]) ).
thf(c_0_209,plain,
( p45
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
thf(c_0_210,plain,
( ~ p879
| ( ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) )
= ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[pax879]) ).
thf(c_0_211,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
thf(c_0_212,plain,
! [X1: a] :
( ( ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ f__2 ) @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) ) )
| ~ p102 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
thf(c_0_213,plain,
! [X1: a] :
( ( f__0 @ f__2 @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ f__2 @ ( f__0 @ f__2 @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160]),c_0_161])]) ).
thf(c_0_214,plain,
( ( f__1 @ f__2 @ ( f__0 @ f__2 @ f__3 ) )
= f__2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_163]),c_0_164]),c_0_165])]) ).
thf(c_0_215,plain,
p102,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_167])]) ).
thf(c_0_216,plain,
! [X1: a] :
( ( ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ f__2 ) @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ X1 ) ) )
| ~ p150 ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
thf(c_0_217,plain,
( ( f__1 @ f__2 @ ( f__0 @ f__2 @ f__4 ) )
= f__2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170]),c_0_164]),c_0_171])]) ).
thf(c_0_218,plain,
p150,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173])]) ).
thf(c_0_219,plain,
! [X1: a] :
( ( ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ f__4 ) @ X1 )
= ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ ( f__0 @ f__4 @ X1 ) ) )
| ~ p535 ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
thf(c_0_220,plain,
! [X1: a] :
( ( f__0 @ f__4 @ X1 )
= ( f__0 @ X1 @ f__4 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_176])]) ).
thf(c_0_221,plain,
! [X1: a] :
( ( f__0 @ X1 @ ( f__1 @ f__2 @ X1 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_178]),c_0_179])]) ).
thf(c_0_222,plain,
p535,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_181])]) ).
thf(c_0_223,plain,
( p879
| ~ p881
| ~ p81 ),
inference(split_conjunct,[status(thm)],[c_0_182]) ).
thf(c_0_224,plain,
p81,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_116])]) ).
thf(c_0_225,plain,
p881,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185])]) ).
thf(c_0_226,plain,
( ~ p93
| p962 ),
inference(fof_simplification,[status(thm)],[ax37]) ).
thf(c_0_227,plain,
( p93
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_186]) ).
thf(c_0_228,plain,
p17,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_91])]) ).
thf(c_0_229,plain,
! [X416: a] :
( ~ p454
| ( ( f__1 @ ( f__1 @ f__2 @ f__2 ) @ X416 )
= ( f__1 @ f__2 @ ( f__1 @ f__2 @ X416 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax454])])]) ).
thf(c_0_230,plain,
! [X1: a] :
( ( ( f__1 @ X1 @ X1 )
= X1 )
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
thf(c_0_231,plain,
p9,
inference(split_conjunct,[status(thm)],[ax1185]) ).
thf(c_0_232,plain,
( p454
| ~ p62 ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
thf(c_0_233,plain,
p62,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_191])]) ).
thf(c_0_234,plain,
! [X814: a,X815: a,X816: a] :
( ~ p7
| ( ( f__1 @ ( f__1 @ X814 @ X815 ) @ X816 )
= ( f__1 @ X814 @ ( f__1 @ X815 @ X816 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])]) ).
thf(c_0_235,plain,
( ~ p59
| p430 ),
inference(fof_simplification,[status(thm)],[ax763]) ).
thf(c_0_236,plain,
( p59
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
thf(c_0_237,plain,
! [X832: a,X833: a] :
( ~ p3
| ( ( f__1 @ ( f__0 @ X832 @ X833 ) @ X833 )
= X833 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])]) ).
thf(c_0_238,plain,
! [X2: a,X1: a] :
( ( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
thf(c_0_239,plain,
! [X564: a] :
( ~ p124
| ( ( f__0 @ f__3 @ ( f__1 @ ( f__0 @ f__3 @ f__4 ) @ X564 ) )
= ( f__1 @ ( f__0 @ f__3 @ ( f__0 @ f__3 @ f__4 ) ) @ ( f__0 @ f__3 @ X564 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax124])])]) ).
thf(c_0_240,plain,
! [X1: a] :
( ( ( f__0 @ ( f__0 @ f__3 @ f__3 ) @ X1 )
= ( f__0 @ f__3 @ ( f__0 @ f__3 @ X1 ) ) )
| ~ p509 ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
thf(c_0_241,plain,
p509,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_196])]) ).
thf(c_0_242,plain,
! [X1: a,X2: a] :
( ( ( f__0 @ f__3 @ ( f__1 @ X1 @ X2 ) )
= ( f__1 @ ( f__0 @ f__3 @ X1 ) @ ( f__0 @ f__3 @ X2 ) ) )
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
thf(c_0_243,plain,
p21,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_91])]) ).
thf(c_0_244,plain,
( p124
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
thf(c_0_245,plain,
! [X1: a,X2: a] :
( ( ( f__0 @ ( f__1 @ X1 @ X2 ) @ X2 )
= X2 )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
thf(c_0_246,plain,
( p1
| ( ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) )
!= ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
thf(c_0_247,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_202]) ).
thf(c_0_248,plain,
( ~ p962
| ( ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ ( f__1 @ f__3 @ f__2 ) )
= ( f__1 @ ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ f__3 ) @ ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ f__2 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax962]) ).
thf(c_0_249,plain,
! [X1: a] :
( ( ( f__0 @ ( f__0 @ f__3 @ ( f__1 @ f__2 @ f__3 ) ) @ X1 )
= ( f__0 @ f__3 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) ) )
| ~ p506 ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
thf(c_0_250,plain,
p506,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_204,c_0_196])]) ).
thf(c_0_251,plain,
! [X1: a] :
( ( ( f__0 @ ( f__0 @ f__2 @ ( f__1 @ f__2 @ f__3 ) ) @ X1 )
= ( f__0 @ f__2 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) ) )
| ~ p514 ),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
thf(c_0_252,plain,
p514,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_207])]) ).
thf(c_0_253,plain,
! [X1: a] :
( ( ( f__1 @ f__3 @ X1 )
= ( f__1 @ X1 @ f__3 ) )
| ~ p45 ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
thf(c_0_254,plain,
p45,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_97])]) ).
thf(c_0_255,plain,
( ( ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) )
= ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) ) )
| ~ p879 ),
inference(split_conjunct,[status(thm)],[c_0_210]) ).
thf(c_0_256,plain,
! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_143])]) ).
thf(c_0_257,plain,
! [X1: a] :
( ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ f__2 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_212,c_0_170]),c_0_213]),c_0_214]),c_0_215])]) ).
thf(c_0_258,plain,
! [X1: a] :
( ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ f__2 @ ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_216,c_0_170]),c_0_213]),c_0_217]),c_0_218])]) ).
thf(c_0_259,plain,
! [X1: a] :
( ( f__0 @ ( f__1 @ f__2 @ f__4 ) @ ( f__0 @ f__4 @ X1 ) )
= ( f__0 @ f__4 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_219,c_0_220]),c_0_221]),c_0_222])]) ).
thf(c_0_260,plain,
p879,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_223,c_0_224]),c_0_225])]) ).
thf(c_0_261,plain,
( p962
| ~ p93 ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
thf(c_0_262,plain,
p93,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_227,c_0_228])]) ).
thf(c_0_263,plain,
! [X464: a] :
( ~ p430
| ( ( f__1 @ ( f__1 @ ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ) @ f__2 ) @ X464 )
= ( f__1 @ ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ) @ ( f__1 @ f__2 @ X464 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax430])])]) ).
thf(c_0_264,plain,
! [X1: a] :
( ( ( f__1 @ ( f__1 @ f__2 @ f__2 ) @ X1 )
= ( f__1 @ f__2 @ ( f__1 @ f__2 @ X1 ) ) )
| ~ p454 ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
thf(c_0_265,plain,
! [X1: a] :
( ( f__1 @ X1 @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_230,c_0_231])]) ).
thf(c_0_266,plain,
p454,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_232,c_0_233])]) ).
thf(c_0_267,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__1 @ ( f__1 @ X1 @ X2 ) @ X3 )
= ( f__1 @ X1 @ ( f__1 @ X2 @ X3 ) ) )
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
thf(c_0_268,plain,
( p430
| ~ p59 ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
thf(c_0_269,plain,
p59,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_236,c_0_191])]) ).
thf(c_0_270,plain,
! [X1: a,X2: a] :
( ( ( f__1 @ ( f__0 @ X1 @ X2 ) @ X2 )
= X2 )
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
thf(c_0_271,plain,
! [X2: a,X1: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_238,c_0_97])]) ).
thf(c_0_272,plain,
! [X1: a] :
( ( ( f__0 @ f__3 @ ( f__1 @ ( f__0 @ f__3 @ f__4 ) @ X1 ) )
= ( f__1 @ ( f__0 @ f__3 @ ( f__0 @ f__3 @ f__4 ) ) @ ( f__0 @ f__3 @ X1 ) ) )
| ~ p124 ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
thf(c_0_273,plain,
! [X1: a] :
( ( f__0 @ f__3 @ ( f__0 @ f__3 @ X1 ) )
= ( f__0 @ f__3 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_160]),c_0_241])]) ).
thf(c_0_274,plain,
! [X1: a,X2: a] :
( ( f__1 @ ( f__0 @ f__3 @ X1 ) @ ( f__0 @ f__3 @ X2 ) )
= ( f__0 @ f__3 @ ( f__1 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_242,c_0_243])]) ).
thf(c_0_275,plain,
p124,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_244,c_0_243])]) ).
thf(c_0_276,plain,
! [X836: a,X837: a,X838: a] :
( ~ p2
| ( ( f__0 @ X836 @ ( f__1 @ X837 @ X838 ) )
= ( f__1 @ ( f__0 @ X836 @ X837 ) @ ( f__0 @ X836 @ X838 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])]) ).
thf(c_0_277,plain,
! [X2: a,X1: a] :
( ( f__0 @ X1 @ ( f__1 @ X2 @ X1 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_245,c_0_178]),c_0_140])]) ).
thf(c_0_278,plain,
( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) )
!= ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ),
inference(sr,[status(thm)],[c_0_246,c_0_247]) ).
thf(c_0_279,plain,
( ( ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ ( f__1 @ f__3 @ f__2 ) )
= ( f__1 @ ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ f__3 ) @ ( f__0 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__1 @ f__2 @ f__4 ) ) @ f__2 ) ) )
| ~ p962 ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
thf(c_0_280,plain,
! [X1: a] :
( ( f__0 @ f__3 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) )
= ( f__0 @ f__3 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_249,c_0_221]),c_0_250])]) ).
thf(c_0_281,plain,
! [X1: a] :
( ( f__0 @ f__2 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ X1 ) )
= ( f__0 @ f__2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_251,c_0_213]),c_0_214]),c_0_252])]) ).
thf(c_0_282,plain,
! [X1: a] :
( ( f__1 @ f__3 @ X1 )
= ( f__1 @ X1 @ f__3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_253,c_0_254])]) ).
thf(c_0_283,plain,
( ( f__1 @ f__2 @ ( f__0 @ ( f__1 @ f__2 @ f__3 ) @ ( f__0 @ f__4 @ ( f__1 @ f__2 @ f__3 ) ) ) )
= ( f__1 @ f__2 @ ( f__0 @ f__4 @ ( f__1 @ f__2 @ f__3 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_255,c_0_256]),c_0_257]),c_0_220]),c_0_258]),c_0_259]),c_0_257]),c_0_257]),c_0_220]),c_0_260])]) ).
thf(c_0_284,plain,
p962,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_261,c_0_262])]) ).
thf(c_0_285,plain,
! [X1: a] :
( ( ( f__1 @ ( f__1 @ ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ) @ f__2 ) @ X1 )
= ( f__1 @ ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ) @ ( f__1 @ f__2 @ X1 ) ) )
| ~ p430 ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
thf(c_0_286,plain,
! [X1: a] :
( ( f__1 @ f__2 @ ( f__1 @ f__2 @ X1 ) )
= ( f__1 @ f__2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_264,c_0_265]),c_0_266])]) ).
thf(c_0_287,plain,
! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__1 @ X1 @ X2 ) @ X3 )
= ( f__1 @ X1 @ ( f__1 @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_267,c_0_191])]) ).
thf(c_0_288,plain,
p430,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_269])]) ).
thf(c_0_289,plain,
! [X2: a,X1: a] :
( ( f__1 @ X1 @ ( f__0 @ X2 @ X1 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_270,c_0_271]),c_0_100])]) ).
thf(c_0_290,plain,
! [X1: a] :
( ( f__0 @ f__3 @ ( f__1 @ ( f__0 @ f__3 @ f__4 ) @ X1 ) )
= ( f__0 @ f__3 @ ( f__1 @ f__4 @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_272,c_0_273]),c_0_274]),c_0_275])]) ).
thf(c_0_291,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
thf(c_0_292,plain,
! [X2: a,X1: a] :
( ( f__0 @ X1 @ ( f__1 @ X1 @ X2 ) )
= X1 ),
inference(spm,[status(thm)],[c_0_277,c_0_271]) ).
thf(c_0_293,plain,
( f__1 @ f__2 @ ( f__0 @ f__4 @ ( f__1 @ f__2 @ f__3 ) ) )
!= ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_278,c_0_257]),c_0_220]) ).
thf(c_0_294,plain,
( ( f__1 @ f__2 @ ( f__0 @ f__4 @ ( f__1 @ f__2 @ f__3 ) ) )
= ( f__1 @ f__2 @ ( f__0 @ f__3 @ ( f__1 @ f__2 @ f__4 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_279,c_0_178]),c_0_280]),c_0_178]),c_0_281]),c_0_213]),c_0_217]),c_0_271]),c_0_257]),c_0_220]),c_0_282]),c_0_178]),c_0_257]),c_0_283]),c_0_284])]) ).
thf(c_0_295,plain,
! [X1: a] :
( ( f__1 @ f__2 @ ( f__1 @ ( f__0 @ f__3 @ f__4 ) @ ( f__1 @ f__2 @ X1 ) ) )
= ( f__1 @ f__2 @ ( f__1 @ ( f__0 @ f__3 @ f__4 ) @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_285,c_0_271]),c_0_286]),c_0_287]),c_0_287]),c_0_288])]) ).
thf(c_0_296,plain,
! [X1: a] :
( ( f__1 @ ( f__0 @ f__3 @ f__4 ) @ ( f__1 @ X1 @ ( f__0 @ f__3 @ ( f__1 @ f__4 @ X1 ) ) ) )
= ( f__1 @ ( f__0 @ f__3 @ f__4 ) @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_290]),c_0_287]) ).
thf(c_0_297,plain,
! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) )
= ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_291,c_0_91])]) ).
thf(c_0_298,plain,
! [X1: a,X2: a] :
( ( f__1 @ X1 @ ( f__1 @ X2 @ X1 ) )
= ( f__1 @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_292]),c_0_287]) ).
thf(c_0_299,plain,
( f__1 @ f__2 @ ( f__0 @ f__3 @ ( f__1 @ f__2 @ f__4 ) ) )
!= ( f__1 @ f__2 @ ( f__0 @ f__3 @ f__4 ) ),
inference(rw,[status(thm)],[c_0_293,c_0_294]) ).
thf(c_0_300,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_295,c_0_296]),c_0_164]),c_0_286]),c_0_164]),c_0_297]),c_0_298]),c_0_164]),c_0_299]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h25,h24,h23,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],]) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h23,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__4)],[h24,1,h25]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__3)],[h23,2,h24]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__2)],[h20,3,h23]) ).
thf(h26,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__0 @ eigen__5 @ ( eigen__1 @ X1 @ X2 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__5 @ X1 ) @ ( eigen__0 @ eigen__5 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ! [X1: a] :
( ( eigen__0 @ eigen__5 @ ( eigen__1 @ eigen__6 @ X1 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__5 @ eigen__6 ) @ ( eigen__0 @ eigen__5 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
( eigen__0 @ eigen__5 @ ( eigen__1 @ eigen__6 @ eigen__7 ) )
!= ( eigen__1 @ ( eigen__0 @ eigen__5 @ eigen__6 ) @ ( eigen__0 @ eigen__5 @ eigen__7 ) ),
introduced(assumption,[]) ).
thf(ax4720,axiom,
( ~ p1001
| p1007 ),
file('<stdin>',ax4720) ).
thf(ax4598,axiom,
( ~ p8
| p1072 ),
file('<stdin>',ax4598) ).
thf(ax4656,axiom,
( ~ p5
| p1047 ),
file('<stdin>',ax4656) ).
thf(pax6_001,axiom,
( p6
=> ! [X1: a,X2: a] :
( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) ) ),
file('<stdin>',pax6) ).
thf(ax4662,axiom,
( ~ p4
| p1041 ),
file('<stdin>',ax4662) ).
thf(ax4694,axiom,
( ~ p3
| p1031 ),
file('<stdin>',ax4694) ).
thf(ax4624,axiom,
( ~ p6
| p1057 ),
file('<stdin>',ax4624) ).
thf(ax4453,axiom,
( ~ p1007
| p1184 ),
file('<stdin>',ax4453) ).
thf(ax4734,axiom,
p1001,
file('<stdin>',ax4734) ).
thf(ax4655,axiom,
( ~ p5
| p1048 ),
file('<stdin>',ax4655) ).
thf(ax4681,axiom,
( ~ p3
| p1033 ),
file('<stdin>',ax4681) ).
thf(ax4723,axiom,
( ~ p1001
| p1004 ),
file('<stdin>',ax4723) ).
thf(pax10_002,axiom,
( p10
=> ! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 ) ),
file('<stdin>',pax10) ).
thf(ax2280,axiom,
( ~ p1072
| p2917 ),
file('<stdin>',ax2280) ).
thf(ax4727,axiom,
p8,
file('<stdin>',ax4727) ).
thf(ax4585,axiom,
( ~ p8
| p1074 ),
file('<stdin>',ax4585) ).
thf(pax1047,axiom,
( p1047
=> ! [X1: a] :
( ( f__1 @ f__6 @ X1 )
= ( f__1 @ X1 @ f__6 ) ) ),
file('<stdin>',pax1047) ).
thf(ax4730,axiom,
p5,
file('<stdin>',ax4730) ).
thf(pax1041,axiom,
( p1041
=> ! [X1: a] :
( ( f__0 @ ( f__1 @ f__7 @ X1 ) @ X1 )
= X1 ) ),
file('<stdin>',pax1041) ).
thf(ax4729,axiom,
p6,
file('<stdin>',ax4729) ).
thf(ax4731,axiom,
p4,
file('<stdin>',ax4731) ).
thf(ax4106,axiom,
( ~ p1031
| p1531 ),
file('<stdin>',ax4106) ).
thf(ax4732,axiom,
p3,
file('<stdin>',ax4732) ).
thf(pax1057,axiom,
( p1057
=> ! [X1: a] :
( ( f__0 @ f__7 @ X1 )
= ( f__0 @ X1 @ f__7 ) ) ),
file('<stdin>',pax1057) ).
thf(ax43,axiom,
( ~ p1184
| p4956 ),
file('<stdin>',ax43) ).
thf(ax4465,axiom,
( ~ p1007
| p1172 ),
file('<stdin>',ax4465) ).
thf(ax4636,axiom,
( ~ p6
| p1056 ),
file('<stdin>',ax4636) ).
thf(ax4695,axiom,
( ~ p3
| p1030 ),
file('<stdin>',ax4695) ).
thf(pax1048,axiom,
( p1048
=> ! [X1: a] :
( ( f__1 @ f__5 @ X1 )
= ( f__1 @ X1 @ f__5 ) ) ),
file('<stdin>',pax1048) ).
thf(ax3857,axiom,
( ~ p1033
| p1692 ),
file('<stdin>',ax3857) ).
thf(ax4637,axiom,
( ~ p6
| p1055 ),
file('<stdin>',ax4637) ).
thf(ax4523,axiom,
( ~ p1004
| p1114 ),
file('<stdin>',ax4523) ).
thf(pax2917,axiom,
( p2917
=> ! [X1: a] :
( ( f__0 @ ( f__0 @ f__5 @ f__5 ) @ X1 )
= ( f__0 @ f__5 @ ( f__0 @ f__5 @ X1 ) ) ) ),
file('<stdin>',pax2917) ).
thf(ax4725,axiom,
p10,
file('<stdin>',ax4725) ).
thf(pax8_003,axiom,
( p8
=> ! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) ),
file('<stdin>',pax8) ).
thf(ax2033,axiom,
( ~ p1074
| p3076 ),
file('<stdin>',ax2033) ).
thf(ax4680,axiom,
( ~ p3
| p1034 ),
file('<stdin>',ax4680) ).
thf(ax4722,axiom,
( ~ p1001
| p1005 ),
file('<stdin>',ax4722) ).
thf(pax1531,axiom,
( p1531
=> ( ( f__1 @ ( f__0 @ f__6 @ ( f__1 @ f__6 @ f__7 ) ) @ ( f__1 @ f__6 @ f__7 ) )
= ( f__1 @ f__6 @ f__7 ) ) ),
file('<stdin>',pax1531) ).
thf(pax4956,axiom,
( p4956
=> ( ( f__1 @ f__6 @ ( f__0 @ f__7 @ f__5 ) )
= ( f__0 @ ( f__1 @ f__6 @ f__7 ) @ ( f__1 @ f__6 @ f__5 ) ) ) ),
file('<stdin>',pax4956) ).
thf(ax273,axiom,
( ~ p1172
| p4726 ),
file('<stdin>',ax273) ).
thf(pax1056,axiom,
( p1056
=> ! [X1: a] :
( ( f__0 @ f__5 @ X1 )
= ( f__0 @ X1 @ f__5 ) ) ),
file('<stdin>',pax1056) ).
thf(ax4123,axiom,
( ~ p1030
| p1514 ),
file('<stdin>',ax4123) ).
thf(pax1692,axiom,
( p1692
=> ( ( f__1 @ ( f__0 @ f__7 @ f__5 ) @ f__5 )
= f__5 ) ),
file('<stdin>',pax1692) ).
thf(pax1055,axiom,
( p1055
=> ! [X1: a] :
( ( f__0 @ f__6 @ X1 )
= ( f__0 @ X1 @ f__6 ) ) ),
file('<stdin>',pax1055) ).
thf(ax1373,axiom,
( ~ p1114
| p3626 ),
file('<stdin>',ax1373) ).
thf(pax3076,axiom,
( p3076
=> ! [X1: a] :
( ( f__0 @ ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ f__5 ) @ X1 )
= ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ X1 ) ) ) ),
file('<stdin>',pax3076) ).
thf(ax3841,axiom,
( ~ p1034
| p1708 ),
file('<stdin>',ax3841) ).
thf(ax4504,axiom,
( ~ p1005
| p1133 ),
file('<stdin>',ax4504) ).
thf(pax5_004,axiom,
( p5
=> ! [X1: a,X2: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ) ),
file('<stdin>',pax5) ).
thf(pax4726,axiom,
( p4726
=> ( ( f__1 @ f__6 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) )
= ( f__0 @ ( f__1 @ f__6 @ f__5 ) @ ( f__1 @ f__6 @ ( f__1 @ f__6 @ f__7 ) ) ) ) ),
file('<stdin>',pax4726) ).
thf(pax1514,axiom,
( p1514
=> ( ( f__1 @ ( f__0 @ ( f__1 @ f__6 @ f__7 ) @ f__5 ) @ f__5 )
= f__5 ) ),
file('<stdin>',pax1514) ).
thf(pax3626,axiom,
( p3626
=> ( ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ ( f__0 @ f__6 @ f__5 ) )
= ( f__0 @ ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ f__6 ) @ ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ f__5 ) ) ) ),
file('<stdin>',pax3626) ).
thf(pax1708,axiom,
( p1708
=> ( ( f__1 @ ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) ) @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) )
= ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) ) ),
file('<stdin>',pax1708) ).
thf(ax1012,axiom,
( ~ p1133
| p3987 ),
file('<stdin>',ax1012) ).
thf(nax1002,axiom,
( p1002
<= ( ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) )
= ( f__1 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ f__7 ) ) ) ),
file('<stdin>',nax1002) ).
thf(ax4733,axiom,
~ p1002,
file('<stdin>',ax4733) ).
thf(pax3987,axiom,
( p3987
=> ( ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ ( f__0 @ f__6 @ f__5 ) )
= ( f__0 @ ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ f__6 ) @ ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ f__5 ) ) ) ),
file('<stdin>',pax3987) ).
thf(c_0_58,plain,
( ~ p1001
| p1007 ),
inference(fof_simplification,[status(thm)],[ax4720]) ).
thf(c_0_59,plain,
( ~ p8
| p1072 ),
inference(fof_simplification,[status(thm)],[ax4598]) ).
thf(c_0_60,plain,
( ~ p5
| p1047 ),
inference(fof_simplification,[status(thm)],[ax4656]) ).
thf(c_0_61,plain,
! [X2904: a,X2905: a] :
( ~ p6
| ( ( f__0 @ X2904 @ X2905 )
= ( f__0 @ X2905 @ X2904 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])]) ).
thf(c_0_62,plain,
( ~ p4
| p1041 ),
inference(fof_simplification,[status(thm)],[ax4662]) ).
thf(c_0_63,plain,
( ~ p3
| p1031 ),
inference(fof_simplification,[status(thm)],[ax4694]) ).
thf(c_0_64,plain,
( ~ p6
| p1057 ),
inference(fof_simplification,[status(thm)],[ax4624]) ).
thf(c_0_65,plain,
( ~ p1007
| p1184 ),
inference(fof_simplification,[status(thm)],[ax4453]) ).
thf(c_0_66,plain,
( p1007
| ~ p1001 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_67,plain,
p1001,
inference(split_conjunct,[status(thm)],[ax4734]) ).
thf(c_0_68,plain,
( ~ p5
| p1048 ),
inference(fof_simplification,[status(thm)],[ax4655]) ).
thf(c_0_69,plain,
( ~ p3
| p1033 ),
inference(fof_simplification,[status(thm)],[ax4681]) ).
thf(c_0_70,plain,
( ~ p1001
| p1004 ),
inference(fof_simplification,[status(thm)],[ax4723]) ).
thf(c_0_71,plain,
! [X2888: a] :
( ~ p10
| ( ( f__0 @ X2888 @ X2888 )
= X2888 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])]) ).
thf(c_0_72,plain,
( ~ p1072
| p2917 ),
inference(fof_simplification,[status(thm)],[ax2280]) ).
thf(c_0_73,plain,
( p1072
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_74,plain,
p8,
inference(split_conjunct,[status(thm)],[ax4727]) ).
thf(c_0_75,plain,
( ~ p8
| p1074 ),
inference(fof_simplification,[status(thm)],[ax4585]) ).
thf(c_0_76,plain,
! [X1960: a] :
( ~ p1047
| ( ( f__1 @ f__6 @ X1960 )
= ( f__1 @ X1960 @ f__6 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1047])])]) ).
thf(c_0_77,plain,
( p1047
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_78,plain,
p5,
inference(split_conjunct,[status(thm)],[ax4730]) ).
thf(c_0_79_005,plain,
! [X1972: a] :
( ~ p1041
| ( ( f__0 @ ( f__1 @ f__7 @ X1972 ) @ X1972 )
= X1972 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1041])])]) ).
thf(c_0_80_006,plain,
! [X2: a,X1: a] :
( ( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) )
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_81_007,plain,
p6,
inference(split_conjunct,[status(thm)],[ax4729]) ).
thf(c_0_82_008,plain,
( p1041
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_83_009,plain,
p4,
inference(split_conjunct,[status(thm)],[ax4731]) ).
thf(c_0_84_010,plain,
( ~ p1031
| p1531 ),
inference(fof_simplification,[status(thm)],[ax4106]) ).
thf(c_0_85_011,plain,
( p1031
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_86_012,plain,
p3,
inference(split_conjunct,[status(thm)],[ax4732]) ).
thf(c_0_87_013,plain,
! [X1940: a] :
( ~ p1057
| ( ( f__0 @ f__7 @ X1940 )
= ( f__0 @ X1940 @ f__7 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1057])])]) ).
thf(c_0_88_014,plain,
( p1057
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_89_015,plain,
( ~ p1184
| p4956 ),
inference(fof_simplification,[status(thm)],[ax43]) ).
thf(c_0_90_016,plain,
( p1184
| ~ p1007 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_91_017,plain,
p1007,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).
thf(c_0_92_018,plain,
( ~ p1007
| p1172 ),
inference(fof_simplification,[status(thm)],[ax4465]) ).
thf(c_0_93_019,plain,
( ~ p6
| p1056 ),
inference(fof_simplification,[status(thm)],[ax4636]) ).
thf(c_0_94_020,plain,
( ~ p3
| p1030 ),
inference(fof_simplification,[status(thm)],[ax4695]) ).
thf(c_0_95_021,plain,
! [X1958: a] :
( ~ p1048
| ( ( f__1 @ f__5 @ X1958 )
= ( f__1 @ X1958 @ f__5 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1048])])]) ).
thf(c_0_96_022,plain,
( p1048
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_97_023,plain,
( ~ p1033
| p1692 ),
inference(fof_simplification,[status(thm)],[ax3857]) ).
thf(c_0_98_024,plain,
( p1033
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_99_025,plain,
( ~ p6
| p1055 ),
inference(fof_simplification,[status(thm)],[ax4637]) ).
thf(c_0_100_026,plain,
( ~ p1004
| p1114 ),
inference(fof_simplification,[status(thm)],[ax4523]) ).
thf(c_0_101_027,plain,
( p1004
| ~ p1001 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_102_028,plain,
! [X404: a] :
( ~ p2917
| ( ( f__0 @ ( f__0 @ f__5 @ f__5 ) @ X404 )
= ( f__0 @ f__5 @ ( f__0 @ f__5 @ X404 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2917])])]) ).
thf(c_0_103_029,plain,
! [X1: a] :
( ( ( f__0 @ X1 @ X1 )
= X1 )
| ~ p10 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_104_030,plain,
p10,
inference(split_conjunct,[status(thm)],[ax4725]) ).
thf(c_0_105_031,plain,
( p2917
| ~ p1072 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
thf(c_0_106_032,plain,
p1072,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).
thf(c_0_107_033,plain,
! [X2892: a,X2893: a,X2894: a] :
( ~ p8
| ( ( f__0 @ ( f__0 @ X2892 @ X2893 ) @ X2894 )
= ( f__0 @ X2892 @ ( f__0 @ X2893 @ X2894 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])]) ).
thf(c_0_108_034,plain,
( ~ p1074
| p3076 ),
inference(fof_simplification,[status(thm)],[ax2033]) ).
thf(c_0_109_035,plain,
( p1074
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_110_036,plain,
( ~ p3
| p1034 ),
inference(fof_simplification,[status(thm)],[ax4680]) ).
thf(c_0_111_037,plain,
( ~ p1001
| p1005 ),
inference(fof_simplification,[status(thm)],[ax4722]) ).
thf(c_0_112_038,plain,
( ~ p1531
| ( ( f__1 @ ( f__0 @ f__6 @ ( f__1 @ f__6 @ f__7 ) ) @ ( f__1 @ f__6 @ f__7 ) )
= ( f__1 @ f__6 @ f__7 ) ) ),
inference(fof_nnf,[status(thm)],[pax1531]) ).
thf(c_0_113_039,plain,
! [X1: a] :
( ( ( f__1 @ f__6 @ X1 )
= ( f__1 @ X1 @ f__6 ) )
| ~ p1047 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_114_040,plain,
p1047,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
thf(c_0_115_041,plain,
! [X1: a] :
( ( ( f__0 @ ( f__1 @ f__7 @ X1 ) @ X1 )
= X1 )
| ~ p1041 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_116_042,plain,
! [X2: a,X1: a] :
( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
thf(c_0_117_043,plain,
p1041,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83])]) ).
thf(c_0_118_044,plain,
( p1531
| ~ p1031 ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_119_045,plain,
p1031,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]) ).
thf(c_0_120_046,plain,
( ~ p4956
| ( ( f__1 @ f__6 @ ( f__0 @ f__7 @ f__5 ) )
= ( f__0 @ ( f__1 @ f__6 @ f__7 ) @ ( f__1 @ f__6 @ f__5 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax4956]) ).
thf(c_0_121_047,plain,
! [X1: a] :
( ( ( f__0 @ f__7 @ X1 )
= ( f__0 @ X1 @ f__7 ) )
| ~ p1057 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
thf(c_0_122_048,plain,
p1057,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_81])]) ).
thf(c_0_123_049,plain,
( p4956
| ~ p1184 ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
thf(c_0_124_050,plain,
p1184,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
thf(c_0_125_051,plain,
( ~ p1172
| p4726 ),
inference(fof_simplification,[status(thm)],[ax273]) ).
thf(c_0_126_052,plain,
( p1172
| ~ p1007 ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
thf(c_0_127_053,plain,
! [X1942: a] :
( ~ p1056
| ( ( f__0 @ f__5 @ X1942 )
= ( f__0 @ X1942 @ f__5 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1056])])]) ).
thf(c_0_128_054,plain,
( p1056
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_129_055,plain,
( ~ p1030
| p1514 ),
inference(fof_simplification,[status(thm)],[ax4123]) ).
thf(c_0_130_056,plain,
( p1030
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
thf(c_0_131_057,plain,
( ~ p1692
| ( ( f__1 @ ( f__0 @ f__7 @ f__5 ) @ f__5 )
= f__5 ) ),
inference(fof_nnf,[status(thm)],[pax1692]) ).
thf(c_0_132_058,plain,
! [X1: a] :
( ( ( f__1 @ f__5 @ X1 )
= ( f__1 @ X1 @ f__5 ) )
| ~ p1048 ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
thf(c_0_133_059,plain,
p1048,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_78])]) ).
thf(c_0_134_060,plain,
( p1692
| ~ p1033 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
thf(c_0_135_061,plain,
p1033,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_86])]) ).
thf(c_0_136_062,plain,
! [X1944: a] :
( ~ p1055
| ( ( f__0 @ f__6 @ X1944 )
= ( f__0 @ X1944 @ f__6 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1055])])]) ).
thf(c_0_137_063,plain,
( p1055
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
thf(c_0_138_064,plain,
( ~ p1114
| p3626 ),
inference(fof_simplification,[status(thm)],[ax1373]) ).
thf(c_0_139_065,plain,
( p1114
| ~ p1004 ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
thf(c_0_140_066,plain,
p1004,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_67])]) ).
thf(c_0_141_067,plain,
! [X86: a] :
( ~ p3076
| ( ( f__0 @ ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ f__5 ) @ X86 )
= ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ X86 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3076])])]) ).
thf(c_0_142_068,plain,
! [X1: a] :
( ( ( f__0 @ ( f__0 @ f__5 @ f__5 ) @ X1 )
= ( f__0 @ f__5 @ ( f__0 @ f__5 @ X1 ) ) )
| ~ p2917 ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
thf(c_0_143_069,plain,
! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).
thf(c_0_144_070,plain,
p2917,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]) ).
thf(c_0_145_071,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
thf(c_0_146_072,plain,
( p3076
| ~ p1074 ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
thf(c_0_147_073,plain,
p1074,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_74])]) ).
thf(c_0_148_074,plain,
( ~ p1034
| p1708 ),
inference(fof_simplification,[status(thm)],[ax3841]) ).
thf(c_0_149_075,plain,
( p1034
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
thf(c_0_150_076,plain,
( ~ p1005
| p1133 ),
inference(fof_simplification,[status(thm)],[ax4504]) ).
thf(c_0_151_077,plain,
( p1005
| ~ p1001 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
thf(c_0_152_078,plain,
! [X2908: a,X2909: a] :
( ~ p5
| ( ( f__1 @ X2908 @ X2909 )
= ( f__1 @ X2909 @ X2908 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_153_079,plain,
( ~ p4726
| ( ( f__1 @ f__6 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) )
= ( f__0 @ ( f__1 @ f__6 @ f__5 ) @ ( f__1 @ f__6 @ ( f__1 @ f__6 @ f__7 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[pax4726]) ).
thf(c_0_154_080,plain,
( ( ( f__1 @ ( f__0 @ f__6 @ ( f__1 @ f__6 @ f__7 ) ) @ ( f__1 @ f__6 @ f__7 ) )
= ( f__1 @ f__6 @ f__7 ) )
| ~ p1531 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_155_081,plain,
! [X1: a] :
( ( f__1 @ f__6 @ X1 )
= ( f__1 @ X1 @ f__6 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
thf(c_0_156_082,plain,
! [X1: a] :
( ( f__0 @ X1 @ ( f__1 @ f__7 @ X1 ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116]),c_0_117])]) ).
thf(c_0_157_083,plain,
p1531,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119])]) ).
thf(c_0_158_084,plain,
( ( ( f__1 @ f__6 @ ( f__0 @ f__7 @ f__5 ) )
= ( f__0 @ ( f__1 @ f__6 @ f__7 ) @ ( f__1 @ f__6 @ f__5 ) ) )
| ~ p4956 ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
thf(c_0_159_085,plain,
! [X1: a] :
( ( f__0 @ f__7 @ X1 )
= ( f__0 @ X1 @ f__7 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122])]) ).
thf(c_0_160_086,plain,
p4956,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
thf(c_0_161_087,plain,
( p4726
| ~ p1172 ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
thf(c_0_162_088,plain,
p1172,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_91])]) ).
thf(c_0_163_089,plain,
( ~ p1514
| ( ( f__1 @ ( f__0 @ ( f__1 @ f__6 @ f__7 ) @ f__5 ) @ f__5 )
= f__5 ) ),
inference(fof_nnf,[status(thm)],[pax1514]) ).
thf(c_0_164_090,plain,
! [X1: a] :
( ( ( f__0 @ f__5 @ X1 )
= ( f__0 @ X1 @ f__5 ) )
| ~ p1056 ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
thf(c_0_165_091,plain,
p1056,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_81])]) ).
thf(c_0_166_092,plain,
( p1514
| ~ p1030 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_167_093,plain,
p1030,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_86])]) ).
thf(c_0_168_094,plain,
( ~ p3626
| ( ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ ( f__0 @ f__6 @ f__5 ) )
= ( f__0 @ ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ f__6 ) @ ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ f__5 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax3626]) ).
thf(c_0_169_095,plain,
( ( ( f__1 @ ( f__0 @ f__7 @ f__5 ) @ f__5 )
= f__5 )
| ~ p1692 ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
thf(c_0_170_096,plain,
! [X1: a] :
( ( f__1 @ f__5 @ X1 )
= ( f__1 @ X1 @ f__5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133])]) ).
thf(c_0_171_097,plain,
p1692,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]) ).
thf(c_0_172_098,plain,
! [X1: a] :
( ( ( f__0 @ f__6 @ X1 )
= ( f__0 @ X1 @ f__6 ) )
| ~ p1055 ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
thf(c_0_173_099,plain,
p1055,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_81])]) ).
thf(c_0_174_100,plain,
( p3626
| ~ p1114 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_175_101,plain,
p1114,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140])]) ).
thf(c_0_176_102,plain,
( ~ p1708
| ( ( f__1 @ ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) ) @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) )
= ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax1708]) ).
thf(c_0_177_103,plain,
! [X1: a] :
( ( ( f__0 @ ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ f__5 ) @ X1 )
= ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ X1 ) ) )
| ~ p3076 ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
thf(c_0_178_104,plain,
! [X1: a] :
( ( f__0 @ f__5 @ ( f__0 @ f__5 @ X1 ) )
= ( f__0 @ f__5 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_143]),c_0_144])]) ).
thf(c_0_179_105,plain,
! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_74])]) ).
thf(c_0_180_106,plain,
p3076,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147])]) ).
thf(c_0_181_107,plain,
( p1708
| ~ p1034 ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
thf(c_0_182_108,plain,
p1034,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_86])]) ).
thf(c_0_183_109,plain,
( ~ p1133
| p3987 ),
inference(fof_simplification,[status(thm)],[ax1012]) ).
thf(c_0_184_110,plain,
( p1133
| ~ p1005 ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
thf(c_0_185_111,plain,
p1005,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_67])]) ).
thf(c_0_186_112,plain,
( ( ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) )
!= ( f__1 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ f__7 ) ) )
| p1002 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1002])]) ).
thf(c_0_187_113,plain,
! [X2: a,X1: a] :
( ( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
thf(c_0_188_114,plain,
~ p1002,
inference(fof_simplification,[status(thm)],[ax4733]) ).
thf(c_0_189_115,plain,
( ~ p3987
| ( ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ ( f__0 @ f__6 @ f__5 ) )
= ( f__0 @ ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ f__6 ) @ ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ f__5 ) ) ) ),
inference(fof_nnf,[status(thm)],[pax3987]) ).
thf(c_0_190_116,plain,
( ( ( f__1 @ f__6 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) )
= ( f__0 @ ( f__1 @ f__6 @ f__5 ) @ ( f__1 @ f__6 @ ( f__1 @ f__6 @ f__7 ) ) ) )
| ~ p4726 ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
thf(c_0_191_117,plain,
( ( f__1 @ f__6 @ ( f__1 @ f__7 @ f__6 ) )
= ( f__1 @ f__7 @ f__6 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_155]),c_0_156]),c_0_155]),c_0_155]),c_0_157])]) ).
thf(c_0_192_118,plain,
( ( f__0 @ ( f__1 @ f__5 @ f__6 ) @ ( f__1 @ f__7 @ f__6 ) )
= ( f__1 @ f__6 @ ( f__0 @ f__5 @ f__7 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_155]),c_0_155]),c_0_116]),c_0_159]),c_0_160])]) ).
thf(c_0_193_119,plain,
p4726,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_162])]) ).
thf(c_0_194_120,plain,
( ( ( f__1 @ ( f__0 @ ( f__1 @ f__6 @ f__7 ) @ f__5 ) @ f__5 )
= f__5 )
| ~ p1514 ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
thf(c_0_195_121,plain,
! [X1: a] :
( ( f__0 @ f__5 @ X1 )
= ( f__0 @ X1 @ f__5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165])]) ).
thf(c_0_196_122,plain,
p1514,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_167])]) ).
thf(c_0_197_123,plain,
( ( ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ ( f__0 @ f__6 @ f__5 ) )
= ( f__0 @ ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ f__6 ) @ ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ f__5 ) ) )
| ~ p3626 ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
thf(c_0_198_124,plain,
( ( f__1 @ f__5 @ ( f__0 @ f__5 @ f__7 ) )
= f__5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_159]),c_0_170]),c_0_171])]) ).
thf(c_0_199_125,plain,
! [X1: a] :
( ( f__0 @ f__6 @ X1 )
= ( f__0 @ X1 @ f__6 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173])]) ).
thf(c_0_200_126,plain,
p3626,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_175])]) ).
thf(c_0_201_127,plain,
( ( ( f__1 @ ( f__0 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) ) @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) )
= ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) )
| ~ p1708 ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_202_128,plain,
! [X1: a] :
( ( f__0 @ f__5 @ ( f__0 @ f__6 @ ( f__0 @ f__5 @ X1 ) ) )
= ( f__0 @ f__5 @ ( f__0 @ f__6 @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_116]),c_0_178]),c_0_179]),c_0_179]),c_0_180])]) ).
thf(c_0_203_129,plain,
p1708,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_182])]) ).
thf(c_0_204_130,plain,
( p3987
| ~ p1133 ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
thf(c_0_205_131,plain,
p1133,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185])]) ).
thf(c_0_206_132,plain,
( p1002
| ( ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) )
!= ( f__1 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ f__7 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_186]) ).
thf(c_0_207_133,plain,
! [X2: a,X1: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_78])]) ).
thf(c_0_208_134,plain,
~ p1002,
inference(split_conjunct,[status(thm)],[c_0_188]) ).
thf(c_0_209_135,plain,
( ( ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ ( f__0 @ f__6 @ f__5 ) )
= ( f__0 @ ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ f__6 ) @ ( f__1 @ ( f__0 @ f__5 @ ( f__1 @ f__6 @ f__7 ) ) @ f__5 ) ) )
| ~ p3987 ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
thf(c_0_210_136,plain,
( ( f__1 @ f__6 @ ( f__0 @ f__5 @ ( f__1 @ f__7 @ f__6 ) ) )
= ( f__1 @ f__6 @ ( f__0 @ f__5 @ f__7 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_155]),c_0_155]),c_0_191]),c_0_192]),c_0_155]),c_0_193])]) ).
thf(c_0_211_137,plain,
( ( f__1 @ f__5 @ ( f__0 @ f__5 @ ( f__1 @ f__7 @ f__6 ) ) )
= f__5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_155]),c_0_195]),c_0_170]),c_0_196])]) ).
thf(c_0_212_138,plain,
( ( f__0 @ f__5 @ ( f__1 @ f__6 @ ( f__0 @ f__5 @ f__7 ) ) )
= ( f__1 @ ( f__0 @ f__5 @ f__7 ) @ ( f__0 @ f__5 @ f__6 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_155]),c_0_170]),c_0_198]),c_0_116]),c_0_199]),c_0_200])]) ).
thf(c_0_213_139,plain,
( ( f__1 @ ( f__0 @ f__5 @ f__6 ) @ ( f__0 @ f__5 @ ( f__1 @ f__7 @ f__6 ) ) )
= ( f__0 @ f__5 @ ( f__1 @ f__7 @ f__6 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_155]),c_0_179]),c_0_202]),c_0_156]),c_0_155]),c_0_155]),c_0_203])]) ).
thf(c_0_214_140,plain,
p3987,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_204,c_0_205])]) ).
thf(c_0_215_141,plain,
( f__1 @ ( f__0 @ f__5 @ f__7 ) @ ( f__0 @ f__5 @ f__6 ) )
!= ( f__0 @ f__5 @ ( f__1 @ f__7 @ f__6 ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_207]),c_0_155]),c_0_208]) ).
thf(c_0_216_142,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_155]),c_0_207]),c_0_210]),c_0_155]),c_0_170]),c_0_211]),c_0_116]),c_0_212]),c_0_155]),c_0_199]),c_0_207]),c_0_213]),c_0_214])]),c_0_215]),
[proof] ).
thf(5,plain,
$false,
inference(eprover,[status(thm),assumptions([h28,h27,h26,h21,h22,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h27,h26,h21,h22,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__7)],[h27,5,h28]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h21,h22,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__6)],[h26,6,h27]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__5)],[h21,7,h26]) ).
thf(9,plain,
$false,
inference(tab_be,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h19,h20]),tab_be(discharge,[h21,h22])],[h4,4,8,h19,h20,h21,h22]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,9,h17,h18]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h13,10,h15,h16]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,11,h13,h14]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,12,h11,h12]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,13,h9,h10]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,14,h7,h8]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,15,h5,h6]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,16,h3,h4]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,17,h2]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,18,h1]) ).
thf(0,theorem,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ( ( ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
= ( ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEV001^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Mon Jun 27 23:37:08 EDT 2022
% 0.13/0.32 % CPUTime :
% 83.35/83.19 % SZS status Theorem
% 83.35/83.19 % Mode: mode484
% 83.35/83.19 % Inferences: 585
% 83.35/83.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------